You know guys, I almost thought about posting another logic puzzle, a real one this time. But since it would be much more complex than this one, I fear that the amount of nit picking (there is such a wonderful Finnish expression for that) would explode the forums ;-).
Simply because Jack is "married" under one sense of the word does not necessarily mean that George is "unmarried" in the sense of the negation of Jack's state. The terminology could be used inconsistently in the problem. So, total clarity requires defining marriage as a binary state which precludes non-persons.
I think it's unreasonable not to assume a term is used consistently throughout a puzzle. For example, what if the "Jack" that is married is not the same "Jack" that is looking at Anne?
The problem is that you have to make a lot of assumptions to make the answer work, at least the way it's worded. I agree, it needed to be worded as a list of statements of fact, followed by a conclusion. Something like:
Assume the following to be true: -Jack, George, and Anne are all people. -People can either be Married (M) or Unmarried (U) -Jack is married; George is unmarried -Jack is looking at Anne; Anne is looking at George
Is a married person looking at an unmarried person?
How about this?
There are three people in an otherwise empty room. We know if two of the people are married or not; Jack is married and George is not. We're not sure about Anne. Jack is looking at Anne, but not at George nor himself, and Anne is looking at George, but not at Jack nor herself. George has his eyes closed, and is looking at nobody.
Given the above, say if the following sentence true, false, or can we not be sure: A married person is looking at an unmarried person.
Still needs a bit of fixing. For one, we must explicitly state that Jack, George and Anne are the people in question. Secondly, I removed some redundant information.
There are three people: Jack, George and Anne. We know that Jack is married and George is not, and that Jack is looking at Anne, while Anne is looking at George.
Given the above, say if the following sentence is true, false, or unknown: A married person is looking at an unmarried person.
Still needs a bit of fixing. For one, we must explicitly state that Jack, George and Anne are the people in question. Secondly, I removed some redundant information.
There are three people: Jack, George and Anne. We know that Jack is married and George is not, and that Jack is looking at Anne, while Anne is looking at George.
Given the above, say if the following sentence is true, false, or unknown: A married person is looking at an unmarried person.
The information is not redundant. The pedantic will say "Who is George looking at? Could he be looking at one of the others?"
Don't you get this? Mr WhaleShark said it needed to be a list of statements. I thought not, and showed it could be written as a scene, which makes it more of a riddle than a logic puzzle, but I attempted to do it with no ambiguity so the logic remains. Saying the room is otherwise empty (except for three people), then listing names when referencing those same people means I could not be referencing anyone else.
Have another go at critiquing my formulation of the puzzle, and see if you can not suck this time.
The information is not redundant. The pedantic will say "Who is George looking at? Could he be looking at one of the others?"
That information is completely irrelevant to the answer. Since we know that either Jack is looking at an unmarried Anne, or a married Anne is looking at an unmarried George, any additional information cannot change the fact that the sentence is already true.
Saying the room is otherwise empty (except for three people), then listing names when referencing those same people means I could not be referencing anyone else.
It's a reasonable assumption that they are the three you are referencing, but I wouldn't say that you're precluded from referencing anyone else. In particular, the joining is a bit weak when it comes to Anne. Just because you said there were three people inside a room doesn't mean you can't reference people outside the room.
The way to state a logic problem that leaves no room for ambiguity is to only use numbers, true, false, and precise mathematical terminology. For example this question on the transitive property.
A = B B = C
True or False: C = A
Not much room for ambiguity there.
The thing is, if the original marriage problem had been presented with this notation, it would not be a puzzle at all, and it's "trickiness" would be non-existent. It is because the reader imagines a real life situation that the solution is obscured.
There are three people in an otherwise empty room. We know if two of the people are married or not; Jack is married and George is not. We're not sure about Anne. Jack is looking at Anne, but not at George nor himself, and Anne is looking at George, but not at Jack nor herself. George has his eyes closed, and is looking at nobody.
Given the above, say if the following sentence true, false, or can we not be sure: A married person is looking at an unmarried person.
That works just fine. I broke it down into statements like I did to be totally clear, but you can obfuscate it a bit.
I agree with cheese that you don't need to say who is not looking at whom. For example, do we need to specify that Anne is not looking at a purple giraffe in the corner? You only need to establish the positive relationships, and by the rules of logic puzzles, you cannot assume anything beyond what is presented.
Here's how I would word it to keep it "tricksy:"
Three people - Jack, George, and Anne - are all standing in an empty room. Jack is married, George is not married, and we don't know whether or not Anne is married. Jack is looking at Anne, and Anne is looking at George. Is a married person looking at an unmarried person?
For example, do we need to specify that Anne is not looking at a purple giraffe in the corner?
Ok, the reason I clearly laid out who is looking at who was because I first thought about formulating the puzzle in the same style of others I've heard. That is, three people standing in a line. But if Jack was at the back of the line looking forward, both Anne and George would be in front and both in view. And then Jack (married) would be looking at George too (unmarried). So, when I stated "Jack is looking at Anne, but not at George" I extended that same clarity to the other people.
Comments
There are three people in an otherwise empty room. We know if two of the people are married or not; Jack is married and George is not. We're not sure about Anne. Jack is looking at Anne, but not at George nor himself, and Anne is looking at George, but not at Jack nor herself. George has his eyes closed, and is looking at nobody.
Given the above, say if the following sentence true, false, or can we not be sure: A married person is looking at an unmarried person.
Have at it.
Don't you get this? Mr WhaleShark said it needed to be a list of statements. I thought not, and showed it could be written as a scene, which makes it more of a riddle than a logic puzzle, but I attempted to do it with no ambiguity so the logic remains. Saying the room is otherwise empty (except for three people), then listing names when referencing those same people means I could not be referencing anyone else.
Have another go at critiquing my formulation of the puzzle, and see if you can not suck this time.
A = B
B = C
True or False: C = A
Not much room for ambiguity there.
The thing is, if the original marriage problem had been presented with this notation, it would not be a puzzle at all, and it's "trickiness" would be non-existent. It is because the reader imagines a real life situation that the solution is obscured.
I agree with cheese that you don't need to say who is not looking at whom. For example, do we need to specify that Anne is not looking at a purple giraffe in the corner? You only need to establish the positive relationships, and by the rules of logic puzzles, you cannot assume anything beyond what is presented.
Here's how I would word it to keep it "tricksy:"
Three people - Jack, George, and Anne - are all standing in an empty room. Jack is married, George is not married, and we don't know whether or not Anne is married. Jack is looking at Anne, and Anne is looking at George. Is a married person looking at an unmarried person?